Hækkunin eða lækkunin án viðauka getur verið samningsbrot.

They come from the nouns:

• hækkun = increase, rise
• lækkun = decrease, reduction

With the ending -in, they become definite:

• hækkunin = the increase
• lækkunin = the decrease

So the sentence is talking about a specific increase or a specific decrease, not just increases and decreases in general.

Because these words are the subject of the sentence, they appear in the nominative case.

Here is the pattern:

• hækkun = an increase
• hækkunin = the increase
• hækkunina = the increase (object form, accusative)

The same applies to lækkun.

So:

• hækkunin eða lækkunin = the increase or the decrease as the subject
• not hækkunina eða lækkunina, because those would be object forms

Because hækkunin eða lækkunin means the increase or the decrease — two singular alternatives joined by eða (or).

In Icelandic, with X eða Y where both are singular, the verb is very often singular too:

• Hækkunin eða lækkunin getur...
• literally: The increase or the decrease can...

The idea is not that both together are doing something, but that either one could count as a breach.

Án means without.

The noun after án takes the genitive case. The base noun is:

• viðauki = addendum, annex, appendix

After án, it becomes:

• án viðauka = without an addendum / without an annex

So this is a good example of a preposition controlling a specific case.

In this sentence, addendum or annex is the better translation.

While viðauki can sometimes correspond to appendix, in legal or business language it often means an extra document attached to an agreement — so:

• viðauki við samning = addendum to a contract
• án viðauka = without an addendum

That fits this sentence much better than the everyday English word appendix.

It is a compound noun:

• samningur = contract, agreement
• samnings- = contract's / of a contract
• brot = break, breach, violation

So samningsbrot literally means something like contract-breach, i.e. breach of contract.

This kind of compound is very common in Icelandic.

Icelandic often prefers compound nouns where English uses a phrase.

So English says:

• breach of contract

But Icelandic often packages that idea into one word:

• samningsbrot

The first part, samnings-, is from the genitive singular of samningur:

• samningur → samnings

That genitive form connects the two parts of the compound.

Because Icelandic does not have a normal indefinite article like English a/an.

So:

• samningsbrot can mean a breach of contract
• depending on context, sometimes just breach of contract as a category

Also, after vera (to be), predicate nouns are often left indefinite when you are classifying something:

• Það er samningsbrot = It is a breach of contract
• ...getur verið samningsbrot = ...can be a breach of contract

Because getur verið expresses possibility, not certainty.

• er samningsbrot = is a breach of contract
• getur verið samningsbrot = can be / may be a breach of contract

That difference matters a lot in legal language. The sentence is not automatically declaring that it is a breach in every case; it is saying that it can amount to one.

The normal reading is that it applies to both:

• the increase or the decrease, without an addendum, can be a breach of contract

In other words, if there is either an increase or a decrease and it is made without an addendum, that can be a breach.

Because the phrase comes after both nouns, English speakers sometimes wonder whether it only attaches to the second one, but in this kind of Icelandic sentence it is usually understood more broadly.

Yes. Icelandic word order is somewhat flexible, especially for emphasis.

For example, you could also say:

• Án viðauka getur hækkunin eða lækkunin verið samningsbrot.

That puts extra focus on án viðauka.

The important thing to notice is that Icelandic usually keeps the finite verb in second position, so after fronting Án viðauka, the verb getur comes next.